﻿using System;
using System.Collections.Generic;
using System.Diagnostics;
using Microsoft.Xna.Framework;

namespace FarseerPhysics.Common.PolygonManipulation
{
  internal enum PolyClipType
  {
    Intersect,
    Union,
    Difference
  }

  public enum PolyClipError
  {
    None,
    DegeneratedOutput,
    NonSimpleInput,
    BrokenResult
  }

  //Clipper contributed by Helge Backhaus

  public static class YuPengClipper
  {
    private const float ClipperEpsilonSquared = 1.192092896e-07f;

    public static List<Vertices> Union(Vertices polygon1, Vertices polygon2, out PolyClipError error)
    {
      return Execute(polygon1, polygon2, PolyClipType.Union, out error);
    }

    public static List<Vertices> Difference(Vertices polygon1, Vertices polygon2, out PolyClipError error)
    {
      return Execute(polygon1, polygon2, PolyClipType.Difference, out error);
    }

    public static List<Vertices> Intersect(Vertices polygon1, Vertices polygon2, out PolyClipError error)
    {
      return Execute(polygon1, polygon2, PolyClipType.Intersect, out error);
    }

    /// <summary>
    /// Implements "A new algorithm for Boolean operations on general polygons" 
    /// available here: http://liama.ia.ac.cn/wiki/_media/user:dong:dong_cg_05.pdf
    /// Merges two polygons, a subject and a clip with the specified operation. Polygons may not be 
    /// self-intersecting.
    /// 
    /// Warning: May yield incorrect results or even crash if polygons contain collinear points.
    /// </summary>
    /// <param name="subject">The subject polygon.</param>
    /// <param name="clip">The clip polygon, which is added, 
    /// substracted or intersected with the subject</param>
    /// <param name="clipType">The operation to be performed. Either
    /// Union, Difference or Intersection.</param>
    /// <param name="error">The error generated (if any)</param>
    /// <returns>A list of closed polygons, which make up the result of the clipping operation.
    /// Outer contours are ordered counter clockwise, holes are ordered clockwise.</returns>
    private static List<Vertices> Execute(Vertices subject, Vertices clip, PolyClipType clipType, out PolyClipError error)
    {
      Debug.Assert(subject.IsSimple() && clip.IsSimple(), "Non simple input!", "Input polygons must be simple (cannot intersect themselves).");

      // Copy polygons
      Vertices slicedSubject;
      Vertices slicedClip;
      // Calculate the intersection and touch points between
      // subject and clip and add them to both
      CalculateIntersections(subject, clip, out slicedSubject, out slicedClip);

      // Translate polygons into upper right quadrant
      // as the algorithm depends on it
      Vector2 lbSubject = subject.GetAABB().LowerBound;
      Vector2 lbClip = clip.GetAABB().LowerBound;
      Vector2 translate;
      Vector2.Min(ref lbSubject, ref lbClip, out translate);
      translate = Vector2.One - translate;
      if (translate != Vector2.Zero)
      {
        slicedSubject.Translate(ref translate);
        slicedClip.Translate(ref translate);
      }

      // Enforce counterclockwise contours
      slicedSubject.ForceCounterClockWise();
      slicedClip.ForceCounterClockWise();

      List<Edge> subjectSimplices;
      List<float> subjectCoeff;
      List<Edge> clipSimplices;
      List<float> clipCoeff;
      // Build simplical chains from the polygons and calculate the
      // the corresponding coefficients
      CalculateSimplicalChain(slicedSubject, out subjectCoeff, out subjectSimplices);
      CalculateSimplicalChain(slicedClip, out clipCoeff, out clipSimplices);

      List<Edge> resultSimplices;

      // Determine the characteristics function for all non-original edges
      // in subject and clip simplical chain and combine the edges contributing
      // to the result, depending on the clipType
      CalculateResultChain(subjectCoeff, subjectSimplices, clipCoeff, clipSimplices, clipType,
                           out resultSimplices);

      List<Vertices> result;
      // Convert result chain back to polygon(s)
      error = BuildPolygonsFromChain(resultSimplices, out result);

      // Reverse the polygon translation from the beginning
      // and remove collinear points from output
      translate *= -1f;
      for (int i = 0; i < result.Count; ++i)
      {
        result[i].Translate(ref translate);
        SimplifyTools.CollinearSimplify(result[i]);
      }
      return result;
    }

    /// <summary>
    /// Calculates all intersections between two polygons.
    /// </summary>
    /// <param name="polygon1">The first polygon.</param>
    /// <param name="polygon2">The second polygon.</param>
    /// <param name="slicedPoly1">Returns the first polygon with added intersection points.</param>
    /// <param name="slicedPoly2">Returns the second polygon with added intersection points.</param>
    private static void CalculateIntersections(Vertices polygon1, Vertices polygon2,
                                               out Vertices slicedPoly1, out Vertices slicedPoly2)
    {
      slicedPoly1 = new Vertices(polygon1);
      slicedPoly2 = new Vertices(polygon2);

      // Iterate through polygon1's edges
      for (int i = 0; i < polygon1.Count; i++)
      {
        // Get edge vertices
        Vector2 a = polygon1[i];
        Vector2 b = polygon1[polygon1.NextIndex(i)];

        // Get intersections between this edge and polygon2
        for (int j = 0; j < polygon2.Count; j++)
        {
          Vector2 c = polygon2[j];
          Vector2 d = polygon2[polygon2.NextIndex(j)];

          Vector2 intersectionPoint;
          // Check if the edges intersect
          if (LineTools.LineIntersect(a, b, c, d, out intersectionPoint))
          {
            // calculate alpha values for sorting multiple intersections points on a edge
            float alpha;
            // Insert intersection point into first polygon
            alpha = GetAlpha(a, b, intersectionPoint);
            if (alpha > 0f && alpha < 1f)
            {
              int index = slicedPoly1.IndexOf(a) + 1;
              while (index < slicedPoly1.Count &&
                     GetAlpha(a, b, slicedPoly1[index]) <= alpha)
              {
                ++index;
              }
              slicedPoly1.Insert(index, intersectionPoint);
            }
            // Insert intersection point into second polygon
            alpha = GetAlpha(c, d, intersectionPoint);
            if (alpha > 0f && alpha < 1f)
            {
              int index = slicedPoly2.IndexOf(c) + 1;
              while (index < slicedPoly2.Count &&
                     GetAlpha(c, d, slicedPoly2[index]) <= alpha)
              {
                ++index;
              }
              slicedPoly2.Insert(index, intersectionPoint);
            }
          }
        }
      }
      // Check for very small edges
      for (int i = 0; i < slicedPoly1.Count; ++i)
      {
        int iNext = slicedPoly1.NextIndex(i);
        //If they are closer than the distance remove vertex
        if ((slicedPoly1[iNext] - slicedPoly1[i]).LengthSquared() <= ClipperEpsilonSquared)
        {
          slicedPoly1.RemoveAt(i);
          --i;
        }
      }
      for (int i = 0; i < slicedPoly2.Count; ++i)
      {
        int iNext = slicedPoly2.NextIndex(i);
        //If they are closer than the distance remove vertex
        if ((slicedPoly2[iNext] - slicedPoly2[i]).LengthSquared() <= ClipperEpsilonSquared)
        {
          slicedPoly2.RemoveAt(i);
          --i;
        }
      }
    }

    /// <summary>
    /// Calculates the simplical chain corresponding to the input polygon.
    /// </summary>
    /// <remarks>Used by method <c>Execute()</c>.</remarks>
    private static void CalculateSimplicalChain(Vertices poly, out List<float> coeff,
                                                out List<Edge> simplicies)
    {
      simplicies = new List<Edge>();
      coeff = new List<float>();
      for (int i = 0; i < poly.Count; ++i)
      {
        simplicies.Add(new Edge(poly[i], poly[poly.NextIndex(i)]));
        coeff.Add(CalculateSimplexCoefficient(Vector2.Zero, poly[i], poly[poly.NextIndex(i)]));
      }
    }

    /// <summary>
    /// Calculates the characteristics function for all edges of
    /// the given simplical chains and builds the result chain.
    /// </summary>
    /// <remarks>Used by method <c>Execute()</c>.</remarks>
    private static void CalculateResultChain(List<float> poly1Coeff, List<Edge> poly1Simplicies,
                                               List<float> poly2Coeff, List<Edge> poly2Simplicies,
                                               PolyClipType clipType, out List<Edge> resultSimplices)
    {
      resultSimplices = new List<Edge>();

      for (int i = 0; i < poly1Simplicies.Count; ++i)
      {
        float edgeCharacter = 0;
        if (poly2Simplicies.Contains(poly1Simplicies[i]))
        {
          edgeCharacter = 1f;
        }
        else if (poly2Simplicies.Contains(-poly1Simplicies[i]) && clipType == PolyClipType.Union)
        {
          edgeCharacter = 1f;
        }
        else
        {
          for (int j = 0; j < poly2Simplicies.Count; ++j)
          {
            if (!poly2Simplicies.Contains(-poly1Simplicies[i]))
            {
              edgeCharacter += CalculateBeta(poly1Simplicies[i].GetCenter(),
                                             poly2Simplicies[j], poly2Coeff[j]);
            }
          }
        }
        if (clipType == PolyClipType.Intersect)
        {
          if (edgeCharacter == 1f)
          {
            resultSimplices.Add(poly1Simplicies[i]);
          }
        }
        else
        {
          if (edgeCharacter == 0f)
          {
            resultSimplices.Add(poly1Simplicies[i]);
          }
        }
      }
      for (int i = 0; i < poly2Simplicies.Count; ++i)
      {
        float edgeCharacter = 0f;
        if (!resultSimplices.Contains(poly2Simplicies[i]) &&
            !resultSimplices.Contains(-poly2Simplicies[i]))
        {
          if (poly1Simplicies.Contains(-poly2Simplicies[i]) && clipType == PolyClipType.Union)
          {
            edgeCharacter = 1f;
          }
          else
          {
            edgeCharacter = 0f;
            for (int j = 0; j < poly1Simplicies.Count; ++j)
            {
              if (!poly1Simplicies.Contains(poly2Simplicies[i]) && !poly1Simplicies.Contains(-poly2Simplicies[i]))
              {
                edgeCharacter += CalculateBeta(poly2Simplicies[i].GetCenter(),
                                               poly1Simplicies[j], poly1Coeff[j]);
              }
            }
            if (clipType == PolyClipType.Intersect || clipType == PolyClipType.Difference)
            {
              if (edgeCharacter == 1f)
              {
                resultSimplices.Add(-poly2Simplicies[i]);
              }
            }
            else
            {
              if (edgeCharacter == 0f)
              {
                resultSimplices.Add(poly2Simplicies[i]);
              }
            }
          }
        }
      }
    }

    /// <summary>
    /// Calculates the polygon(s) from the result simplical chain.
    /// </summary>
    /// <remarks>Used by method <c>Execute()</c>.</remarks>
    private static PolyClipError BuildPolygonsFromChain(List<Edge> simplicies, out List<Vertices> result)
    {
      result = new List<Vertices>();
      PolyClipError errVal = PolyClipError.None;

      while (simplicies.Count > 0)
      {
        Vertices output = new Vertices();
        output.Add(simplicies[0].EdgeStart);
        output.Add(simplicies[0].EdgeEnd);
        simplicies.RemoveAt(0);
        bool closed = false;
        int index = 0;
        int count = simplicies.Count; // Needed to catch infinite loops
        while (!closed && simplicies.Count > 0)
        {
          if (VectorEqual(output[output.Count - 1], simplicies[index].EdgeStart))
          {
            if (VectorEqual(simplicies[index].EdgeEnd, output[0]))
            {
              closed = true;
            }
            else
            {
              output.Add(simplicies[index].EdgeEnd);
            }
            simplicies.RemoveAt(index);
            --index;
          }
          else if (VectorEqual(output[output.Count - 1], simplicies[index].EdgeEnd))
          {
            if (VectorEqual(simplicies[index].EdgeStart, output[0]))
            {
              closed = true;
            }
            else
            {
              output.Add(simplicies[index].EdgeStart);
            }
            simplicies.RemoveAt(index);
            --index;
          }
          if (!closed)
          {
            if (++index == simplicies.Count)
            {
              if (count == simplicies.Count)
              {
                result = new List<Vertices>();
                Debug.WriteLine("Undefined error while building result polygon(s).");
                return PolyClipError.BrokenResult;
              }
              index = 0;
              count = simplicies.Count;
            }
          }
        }
        if (output.Count < 3)
        {
          errVal = PolyClipError.DegeneratedOutput;
          Debug.WriteLine("Degenerated output polygon produced (vertices < 3).");
        }
        result.Add(output);
      }
      return errVal;
    }

    /// <summary>
    /// Needed to calculate the characteristics function of a simplex.
    /// </summary>
    /// <remarks>Used by method <c>CalculateEdgeCharacter()</c>.</remarks>
    private static float CalculateBeta(Vector2 point, Edge e, float coefficient)
    {
      float result = 0f;
      if (PointInSimplex(point, e))
      {
        result = coefficient;
      }
      if (PointOnLineSegment(Vector2.Zero, e.EdgeStart, point) ||
          PointOnLineSegment(Vector2.Zero, e.EdgeEnd, point))
      {
        result = .5f * coefficient;
      }
      return result;
    }

    /// <summary>
    /// Needed for sorting multiple intersections points on the same edge.
    /// </summary>
    /// <remarks>Used by method <c>CalculateIntersections()</c>.</remarks>
    private static float GetAlpha(Vector2 start, Vector2 end, Vector2 point)
    {
      return (point - start).LengthSquared() / (end - start).LengthSquared();
    }

    /// <summary>
    /// Returns the coefficient of a simplex.
    /// </summary>
    /// <remarks>Used by method <c>CalculateSimplicalChain()</c>.</remarks>
    private static float CalculateSimplexCoefficient(Vector2 a, Vector2 b, Vector2 c)
    {
      float isLeft = MathUtils.Area(ref a, ref b, ref c);
      if (isLeft < 0f)
      {
        return -1f;
      }

      if (isLeft > 0f)
      {
        return 1f;
      }

      return 0f;
    }

    /// <summary>
    /// Winding number test for a point in a simplex.
    /// </summary>
    /// <param name="point">The point to be tested.</param>
    /// <param name="edge">The edge that the point is tested against.</param>
    /// <returns>False if the winding number is even and the point is outside
    /// the simplex and True otherwise.</returns>
    private static bool PointInSimplex(Vector2 point, Edge edge)
    {
      Vertices polygon = new Vertices();
      polygon.Add(Vector2.Zero);
      polygon.Add(edge.EdgeStart);
      polygon.Add(edge.EdgeEnd);
      return (polygon.PointInPolygon(ref point) == 1);
    }

    /// <summary>
    /// Tests if a point lies on a line segment.
    /// </summary>
    /// <remarks>Used by method <c>CalculateBeta()</c>.</remarks>
    private static bool PointOnLineSegment(Vector2 start, Vector2 end, Vector2 point)
    {
      Vector2 segment = end - start;
      return MathUtils.Area(ref start, ref end, ref point) == 0f &&
             Vector2.Dot(point - start, segment) >= 0f &&
             Vector2.Dot(point - end, segment) <= 0f;
    }

    private static bool VectorEqual(Vector2 vec1, Vector2 vec2)
    {
      return (vec2 - vec1).LengthSquared() <= ClipperEpsilonSquared;
    }

    #region Nested type: Edge

    /// <summary>Specifies an Edge. Edges are used to represent simplicies in simplical chains</summary>
    private sealed class Edge
    {
      public Edge(Vector2 edgeStart, Vector2 edgeEnd)
      {
        EdgeStart = edgeStart;
        EdgeEnd = edgeEnd;
      }

      public Vector2 EdgeStart { get; private set; }
      public Vector2 EdgeEnd { get; private set; }

      public Vector2 GetCenter()
      {
        return (EdgeStart + EdgeEnd) / 2f;
      }

      public static Edge operator -(Edge e)
      {
        return new Edge(e.EdgeEnd, e.EdgeStart);
      }

      public override bool Equals(Object obj)
      {
        // If parameter is null return false.
        if (obj == null)
        {
          return false;
        }

        // If parameter cannot be cast to Point return false.
        return Equals(obj as Edge);
      }

      public bool Equals(Edge e)
      {
        // If parameter is null return false:
        if (e == null)
        {
          return false;
        }

        // Return true if the fields match
        return VectorEqual(EdgeStart, e.EdgeStart) && VectorEqual(EdgeEnd, e.EdgeEnd);
      }

      public override int GetHashCode()
      {
        return EdgeStart.GetHashCode() ^ EdgeEnd.GetHashCode();
      }
    }

    #endregion
  }
}